32 CREATIVE EVOLUTION [chap. 



can achieve is the working of the completed results into 

 a new scheme of the whole, by relation to which they 

 become instantaneous and motionless views taken at in- 

 tervals along the continuity of a movement. Such, for 

 example, is the relation of modern to ancient geometry. 

 The latter, purely static, worked with figures drawn once 

 for all; the former studies the varying of a function — 

 that is, the continuous movement by which the figure 

 is described. No doubt, for greater strictness, all con- 

 siderations of motion may be eliminated from mathe- 

 matical processes; but the introduction of motion into the 

 genesis of figures is nevertheless the origin of modern 

 mathematics. We believe that if biology could ever get 

 as close to its object as mathematics does to its own, it 

 would become, to the physics and chemistry of organized 

 bodies, what the mathematics of the moderns has proved 

 to be in relation to ancient geometry. The wholly super- 

 ficial displacements of masses and molecules studied in 

 physics and chemistry would become, by relation to that 

 inner vital movement (which is transformation and not 

 translation) what the position of a moving object is to the 

 movement of that object in space. And, so far as we can 

 see, the procedure by which we should then pass from the 

 definition of a certain vital action to the system of physico- 

 chemical facts which it implies would be like passing from 

 the function to its derivative, from the equation of the 

 curve (i.e. the law of the continuous movement by which 

 the curve is generated) to the equation of the tangent 

 giving its instantaneous direction. Such a science would 

 be a mechanics of transformation, of which our mechanics 

 of translation would become a particular case, a simpli- 

 fication, a projection on the plane of pure quantity. And 

 just as an infinity of functions have the same differential, 

 these functions differing from each other by a constant, 



